On the convergence theory of double K -weak splittings of type II

Vaibhav Shekhar; Nachiketa Mishra; Debasisha Mishra

Applications of Mathematics (2022)

  • Volume: 67, Issue: 3, page 341-369
  • ISSN: 0862-7940

Abstract

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Recently, Wang (2017) has introduced the K -nonnegative double splitting using the notion of matrices that leave a cone K ⊆ ℝ n invariant and studied its convergence theory by generalizing the corresponding results for the nonnegative double splitting by Song and Song (2011). However, the convergence theory for K -weak regular and K -nonnegative double splittings of type II is not yet studied. In this article, we first introduce this class of splittings and then discuss the convergence theory for these sub-classes of matrices. We then obtain the comparison results for two double splittings of a K -monotone matrix. Most of these results are completely new even for K = ℝ + n . The convergence behavior is discussed by performing numerical experiments for different matrices derived from the discretized Poisson equation.

How to cite

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Shekhar, Vaibhav, Mishra, Nachiketa, and Mishra, Debasisha. "On the convergence theory of double $K$-weak splittings of type II." Applications of Mathematics 67.3 (2022): 341-369. <http://eudml.org/doc/297978>.

@article{Shekhar2022,
abstract = {Recently, Wang (2017) has introduced the $K$-nonnegative double splitting using the notion of matrices that leave a cone $K\subseteq \mathbb \{R\}^\{n\}$ invariant and studied its convergence theory by generalizing the corresponding results for the nonnegative double splitting by Song and Song (2011). However, the convergence theory for $K$-weak regular and $K$-nonnegative double splittings of type II is not yet studied. In this article, we first introduce this class of splittings and then discuss the convergence theory for these sub-classes of matrices. We then obtain the comparison results for two double splittings of a $K$-monotone matrix. Most of these results are completely new even for $K= \mathbb \{R\}^\{n\}_+$. The convergence behavior is discussed by performing numerical experiments for different matrices derived from the discretized Poisson equation.},
author = {Shekhar, Vaibhav, Mishra, Nachiketa, Mishra, Debasisha},
journal = {Applications of Mathematics},
keywords = {linear system; iterative method; $K$-nonnegativity; double splitting; convergence theorem; comparison theorem},
language = {eng},
number = {3},
pages = {341-369},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the convergence theory of double $K$-weak splittings of type II},
url = {http://eudml.org/doc/297978},
volume = {67},
year = {2022},
}

TY - JOUR
AU - Shekhar, Vaibhav
AU - Mishra, Nachiketa
AU - Mishra, Debasisha
TI - On the convergence theory of double $K$-weak splittings of type II
JO - Applications of Mathematics
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 3
SP - 341
EP - 369
AB - Recently, Wang (2017) has introduced the $K$-nonnegative double splitting using the notion of matrices that leave a cone $K\subseteq \mathbb {R}^{n}$ invariant and studied its convergence theory by generalizing the corresponding results for the nonnegative double splitting by Song and Song (2011). However, the convergence theory for $K$-weak regular and $K$-nonnegative double splittings of type II is not yet studied. In this article, we first introduce this class of splittings and then discuss the convergence theory for these sub-classes of matrices. We then obtain the comparison results for two double splittings of a $K$-monotone matrix. Most of these results are completely new even for $K= \mathbb {R}^{n}_+$. The convergence behavior is discussed by performing numerical experiments for different matrices derived from the discretized Poisson equation.
LA - eng
KW - linear system; iterative method; $K$-nonnegativity; double splitting; convergence theorem; comparison theorem
UR - http://eudml.org/doc/297978
ER -

References

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